We propose the first comprehensive characterization of sequence space around an ancestral protein. This work will 1) characterize the effects on function of all possible mutations and pairs of mutations across the protein's entire length and of all possible combinations of mutations at a key subset of sites, 2) illuminate how the distribution of function through this multidimensional sequence space would have affected the processes of protein evolution (a key goal in molecular evolution), and 3) quantify the complete set of main-effect and epistatic genetic determinants of DNA specificity in a transcription factor and elucidate their biochemical causes ? an important goal for protein biochemistry and molecular gene regulation. We use the steroid hormone receptor DNA-binding domain as an ideal model system, because it is of great biomedical importance; it is experimentally and phylogenetically tractable; and its specificity for DNA targets diversified through a well-understood evolutionary process, with a known set of historical mutations and biophysical mechanisms. The proposed work will reveal why this history occurred relative to the many other mutational trajectories the protein could have taken as it evolved its new specificity. With the map of sequence space in hand, we will then apply locus-specific, replicated experimental evolution to the ancestral protein, placing it under strong selection to explore sequence space and evolve the same novel specificity that it acquired during historical evolution. By identifying commonalities and differences among the historical trajectory, experimental evolution trajectories, and the many other possible pathways through sequence space, we will gain fundamental insight into the roles of contingency and determinism in evolution and illuminate underlying mechanistic factors that caused those phenomena. Specific questions include: how many ways were there to evolve the derived DNA specificity, and how many were accessible under selection and drift? Did the historical outcome evolve because it was the optimal genotype, because it was the best or only accessible genotype, or simply due to chance? If more optimal genotypes exist, what prevented the evolving protein from reaching them? To what extent must new specificities evolve through promiscuous intermediates, and how many mutations does it take to evolve a new specificity? We will also characterize sequence space and experimental evolutionary trajectories around ancient receptors that existed at different times during history; this will reveal how the protein's evolvability and robustness fluctuated over evolutionary time due to epistatically acting mutations. Finally, by fully characterizing the main and epistatic genetic determinants of the protein's DNA specificity, we will identify common biophysical mechanisms that underlie DNA recognition, contributing to an important goal in molecular biology, biochemistry, cell biology, and development. The methods and conceptual tools we develop will be applicable to studying other transcription factors and the evolution of many other protein families.